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Unit 1

1.3 Point Charges - Fields & Potentials

2 min readโ€ขnovember 3, 2020

peter57616

Peter Apps


Electric Fields & Work

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https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-lQGeAJwZAQwU.PNG?alt=media&token=ee50682f-f58c-4e74-ba35-8ecbf67112e9
Electric Potential Energy can also be expressed in terms of the Electric Field Strength
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Review Note: Conservation of Energy applies here too!

Potential Difference

Let's take a closer look at that last energy equation we derived. Rearranging it a bit, we get:
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The left-hand side of this equation shows the work (or amount of energy) per unit of charge. This "work per charge" quantity is called electric potential or voltage (V).
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Caution:
W or Ue is electric potential energy, measured in Joules. It is NOT the same as potential difference, V, measured in Joules/Coulomb.
Like energy, voltage is a SCALAR. The change may be positive or negative, but that doesn't imply directionality!
Electric Potential of a Point Charge
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Since the electric field strength decreases as the radius increases, the voltage must also be decreasing as we travel further away from the charge.
We can determine the change in voltage by doing some calculus. Let's imagine traveling away from the charge from radius a to radius b.
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Try using the PhET simulation to create your own fields and notice the how the voltage and equipotential lines change as a function of charge and distance.
Other connections: The idea of equipotential lines with voltage is very similar to topographical maps or barometric pressure maps you may have created in an Earth Science class. In each case, the lines drawn represent areas with the same value: height for topographical maps and pressure for barometric pressure maps
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Image from Wikipedia

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Image from openstax.org

Practice Questions:

1.
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Image from Collegeboard.org

Answer:

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2.
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Image from Collegeboard.org

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-d9fcMJTXAPWH.PNG?alt=media&token=d2f5e5f6-7d45-48e9-8db9-7905952f162d

Answer: a) The Electric Field Lines point from high potential to low potential and are perpendicular to the equipotential lines. Therefore at point A, the electric field line points up and to the right
b) E is the greatest where the V lines are closest together (largest gradient). This happens at B.
c)
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